Heat oil in a large skillet over high heat. Add onion; cook and stir until soft and translucent, about 4 minutes. Add bell pepper and cook until softened, about 3 minutes.

Stir chicken livers into skillet. Cook until livers release their moisture and brown, about 5 minutes.

Sprinkle cumin, chili powder, black pepper, and salt over the liver. Stir until fragrant, 1 to 2 minutes. Add pomegranate molasses and stir until flavors combine, about 2 minutes.

Serve chicken livers hot garnished with chopped parsley.